Time-Varying Optimization on Multiplex Networks: A Novel Two-Stage Distributed Preset-Time Approach

This study investigates distributed time-varying optimization on multiplex networks, presenting a more comprehensive framework than single-layer ones. By leveraging the supra-Laplacian matrix, time-regulator function and zero-gradient-sum method, we develop an innovative two-stage distributed algorithm with preset-time convergence to address the time-varying optimization problem on multiplex networks. The initial stage of the algorithm is devoted to reaching the optimal solution of all local time-varying cost functions within the preset time. Subsequently, the second stage of the algorithm aims to reach the global optimal solution within the preset time, while ensuring that the sum of all gradients remains zero. The validity and efficacy of our theoretical results are substantiated through a series of numerical experiments.